On Cournot and Bertrand competition in collusive mixed oligopolies

We consider a mixed oligopoly of one public and N private firms where goods are horizontally differentiated. In our setting, an interdependent payoff structure characterizes the degree of collusion among private firms. We show that, whereas in the Bertrand model, private firms are willing to collude as much as possible, in the Cournot model, the existence of a public firm reduces the scope of collusion. We also prove that the classic discussion comparing price and quantity competition crucially depends on market collusion. More precisely, price competition unambiguously yields larger profits for private firms only if collusion is high enough. In an infinitely repeated game, we prove that collusion is easier to sustain in a larger oligopoly because, in this case, a larger N helps mitigate the effect of the public firm on private firms’ collusion sustainability. Finally, we also find that collusion is always more easily sustained in the Bertrand case than in the Cournot case.